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vpde_2019-20-diary [2020/02/06 13:40] trinh |
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| * Line integrals (Chap. 3) | * Line integrals (Chap. 3) | ||
| + | We reviewed key notions of Riemann integration (the idea of adding up infinitesimal elements), then started investigating the notion of a scalar line integral. | ||
| + | ==== Lecture 3 (7 Feb 2020) ==== | ||
| + | * A continued look at Chapter 3 (line integrals) | ||
| + | We covered the computation of scalar integrals and work integrals, doing examples for both. We also covered various properties of curves (reversability, | ||
| + | ===== Week 2 ===== | ||
| + | ==== Lecture 4 (11 Feb 2020) ==== | ||
| + | * **Announcements: | ||
| + | * Chap 2: definition of conservative fields | ||
| + | * Chap 4: link of conservative fields and work integrals | ||
| + | |||
| + | We discussed the definition of conservative fields, and covered the important (BIG) theorem on conservative forces, and discussed its importance in the computation of work integrals. We ended with a result linking work integrals with change in kinetic energy (to be completed in lecture 5). | ||
| + | |||
| + | ==== Lecture 5 (13 Feb 2020) ==== | ||
| + | * Chap 4: Finishing up the result on work integrals and kinetic energy | ||
| + | * Chap 5: Parameterisation of surfaces | ||
| + | |||
| + | We discussed how surfaces can be parameterised, | ||
| + | |||
| + | ==== Lecture 6 (14 Feb 2020) ==== | ||
| + | * Chap 5: Finished the proof to the final Lemma about normals to surfaces | ||
| + | * Chap 6: Stated the two main results (flux integral and surface integral) | ||
| + | |||
| + | We discussed how to interpret surface integrals, and how to calculate the two main surface integrals (a scalar one and a vector one). This involved writing dS as a cross product. We did an example with a sphere. | ||
| + | |||
| + | ===== Week 3 ===== | ||
| + | |||
| + | ==== Lecture 7 (18 Feb 2020) ==== | ||
| + | |||
| + | * A short statement and discussion about the strikes. See the Owen Jones' article [[https:// | ||
| + | * Explanation of the surface integral formula | ||
| + | * Thinking about flux integrals and their interpretation (see [[https:// | ||
| + | * Chap. 7: Divergence and curl | ||
| + | |||
| + | ==== Lecture 8 (20 Feb 2020) ==== | ||
| + | * Finishing up the curl and divergence | ||
| + | * Doing more examples on (i) the computation of surfaces and normals; (ii) the computation of flux integrals | ||
| + | |||
| + | ==== Lecture 9 (21 Feb 2020) ==== | ||
| + | * Continued examples on (i) the computation of surfaces and normals; (ii) the computation of flux integrals | ||